Of the five quadratics listed below, four of them have two distinct roots. The fifth quadratic has a repeated root. Find the value of the repeated root.

The value of the repeated root. is x=0.60

see the explanation

Step-by-step explanation:

we know that

In a quadratic equation of the form

The discriminant is equal to

If D=0 ----> The quadratic equation has repeated root

If D>0 ----> The quadratic equation has two different real  solutions

If D<0 ----> The quadratic equation has two different complex  solutions

Verify each case

step 1

we have

To find the roots equate the equation to zero

so

Find the discriminant D

therefore

The quadratic equation has two distinct roots

step 2

we have

To find the roots equate the equation to zero

so

Find the discriminant D

therefore

The quadratic equation has two distinct roots

step 3

we have

To find the roots equate the equation to zero

so

Find the discriminant D

therefore

The quadratic equation has two distinct roots

step 4

we have

To find the roots equate the equation to zero

so

Find the discriminant D

therefore

The quadratic equation has repeated roots

step 5

Find the value of the repeated root

The formula to solve a quadratic equation of the form

is equal to

we have

substitute

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.